Z Test for Known Population Standard Deviation
Compute the test of hypothesis and compute confidence interval on the mean of a population when the standard deviation of the population is known.
ZTest(x, ...)
## Default S3 method:
ZTest(x, y = NULL, alternative = c("two.sided", "less", "greater"),
paired = FALSE, mu = 0, sd_pop, conf.level = 0.95, ... )
## S3 method for class 'formula'
ZTest(formula, data, subset, na.action, ...)x |
numeric vector of data values. Non-finite (e.g. infinite or missing) values will be omitted. |
y |
an optional numeric vector of data values: as with x non-finite values will be omitted. |
mu |
a number specifying the hypothesized mean of the population. |
sd_pop |
a number specifying the known standard deviation of the population. |
alternative |
a character string specifying the alternative
hypothesis, must be one of |
paired |
a logical indicating whether you want a paired z-test. |
conf.level |
confidence level for the interval computation. |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see |
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when the data contain |
... |
further arguments to be passed to or from methods. |
Most introductory statistical texts introduce inference by using the z-test
and z-based confidence intervals based on knowing the population
standard deviation. However statistical packages often do not include
functions to do z-tests since the t-test is usually more appropriate
for real world situations. This function is meant to be used during
that short period of learning when the student is learning about
inference using z-procedures, but has not learned the t-based
procedures yet. Once the student has learned about the
t-distribution the t.test() function should be used instead of this
one (but the syntax is very similar, so this function should be an
appropriate introductory step to learning t.test()).
The formula interface is only applicable for the 2-sample tests.
A list with class "htest" containing the following components:
statistic |
the value of the z-statistic. |
p.value |
the p-value for the test |
conf.int |
a confidence interval for the mean appropriate to the specified alternative hypothesis. |
estimate |
the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test. |
null.value |
the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
Andri Signorell <andri@signorell.net>, based on R-Core code of t.test,
documentation partly from Greg Snow <greg.snow@imail.org>
Stahel, W. (2002) Statistische Datenanalyse, 4th ed, vieweg
x <- rnorm(25, 100, 5)
ZTest(x, mu=99, sd_pop=5)
# the classic interface
with(sleep, ZTest(extra[group == 1], extra[group == 2], sd_pop=2))
# the formula interface
ZTest(extra ~ group, data = sleep, sd_pop=2)
# Stahel (2002), pp. 186, 196
d.tyres <- data.frame(A=c(44.5,55,52.5,50.2,45.3,46.1,52.1,50.5,50.6,49.2),
B=c(44.9,54.8,55.6,55.2,55.6,47.7,53,49.1,52.3,50.7))
with(d.tyres, ZTest(A, B, sd_pop=3, paired=TRUE))
d.oxen <- data.frame(ext=c(2.7,2.7,1.1,3.0,1.9,3.0,3.8,3.8,0.3,1.9,1.9),
int=c(6.5,5.4,8.1,3.5,0.5,3.8,6.8,4.9,9.5,6.2,4.1))
with(d.oxen, ZTest(int, ext, sd_pop=1.8, paired=FALSE))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.